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Definition df-op 3674
Description: Define the type-level ordered pair. Definition from {{Rosser}}, p. 281.
Assertion
Ref Expression
df-op A, B = ({x y A x = Phi y} ∪ {x y B x = ( Phi y ∪ {0c})})
Distinct variable groups:   x,y,A   x,B,y

Detailed syntax breakdown of Definition df-op
StepHypRef Expression
1 cA . . 3 class A
2 cB . . 3 class B
31, 2cop 3669 . 2 class A, B
4 vx . . . . . . 7 set x
54cv 1397 . . . . . 6 class x
6 vy . . . . . . . 8 set y
76cv 1397 . . . . . . 7 class y
87cphi 3670 . . . . . 6 class Phi y
95, 8wceq 1398 . . . . 5 wff x = Phi y
109, 6, 1wrex 2104 . . . 4 wff y A x = Phi y
1110, 4cab 1882 . . 3 class {x y A x = Phi y}
12 c0c 3482 . . . . . . . 8 class 0c
1312csn 2803 . . . . . . 7 class {0c}
148, 13cun 2609 . . . . . 6 class ( Phi y ∪ {0c})
155, 14wceq 1398 . . . . 5 wff x = ( Phi y ∪ {0c})
1615, 6, 2wrex 2104 . . . 4 wff y B x = ( Phi y ∪ {0c})
1716, 4cab 1882 . . 3 class {x y B x = ( Phi y ∪ {0c})}
1811, 17cun 2609 . 2 class ({x y A x = Phi y} ∪ {x y B x = ( Phi y ∪ {0c})})
193, 18wceq 1398 1 wff A, B = ({x y A x = Phi y} ∪ {x y B x = ( Phi y ∪ {0c})})
Colors of variables: wff set class
This definition is referenced by:  dfop2  3683  proj1op  3706  proj2op  3707  hbop  3710  eqop  3717  dfswap2  3839  elopprim  5506
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